This problem was caused by the initial decision of limiting each search index to a single entity (or other) type – since normal searches are always executed on a single index, a search across multiple types cannot be created this way. While other, maybe better-working workarounds in Drupal 7 would be possible, this is solved completely in Drupal 8 where this restriction doesn’t exist anymore.

Sarah Meeks, 28, and her 30-year-old brother, Thomas Meeks — founders of SeeqIt LLC (pronounced seek-it) —have been working on a new search engine called Trevinly. The idea is relatively basic: No more search-engine optimization. Businesses would pay SeeqIt $9 a month or $99 a year, and the site’s fairness algorithm guarantees distributed first place rankings. There's also a freemium version of the site, which doesn't have photos for businesses.

Use the Computed Field module to create yet another field stored in the database, combining the two (or more) fields you want to search, then expose a filter for that field instead of both of the individual fields. (I don't like this because it duplicates content/storage, and involves an extra module to do so).